Electronic Proceedings of the 13th Asian Technology Conference in Mathematics

 ISSN 1940-2279 (CD) and ISSN 1940-4204 (Online)

 

Abstract for 14755
Applied problems with Geometry Expressions
Authors: Philip Todd
Affiliations: Saltire Software
Keywords:

In this workshop we will address two applied problems using Geometry Expressions:
1. Finding the focal surface of a parabolic reflector. Light parallel to the axis of symmetry of a parabolic mirror reflects to a precise focus. The reflected rays of parallel beams of light which are incident at an angle to the mirror’s axis do not meet at a point. However, they are concentrated by the mirror in a specific region. We use Geometry Expressions to model the geometric optics, we apply appropriate mathematical approximations, and derive the focal surface of the mirror.
2. Creating a cam profile for a given follower motion. Cams are used in mechanical engineering. An off-centered circular cam with a reciprocating flat face follower produces sinusoidal output. We model this in Geometry Expressions, then find out what happens if the flat face is replaced by a roller follower. We then work out what shape of cam will recover the original sinusoidal motion.
Some experience with Geometry Expressions, or participation in one of the beginner workshops is recommended, as advanced Geometry Expressions techniques will be explored.